What did he do in the previous 4 hands? Even if it's nothing, that's something.

What hands does he check with? Which of those hands check/call? Which of those hands check/fold? If he check/raises, can you stack off? How will certain turn cards (K, backdoor flush card, back door straight card, bottom card pairing, you making a full house, otherwise blank card) affect your equity against his range? If you do check behind, and he bets, what hands does he check on the flop and bet the turn with? Is he capable of a bluff here? Is he capable of check-raising the flop with worse than AQ, then bet/calling a raise on the turn?